A popular modification to the blob problem is to consider the case where the upper plate is uniformly lifted in time such that \(b \rightarrow b(t)\) . The volume of viscous fluid remains constant (\(Q = 0\) ) so that when the plates are separated, this results in fingers developing inward. For this configuration, the governing equation for pressure (REF ) becomes Poisson's equation. However, pressure can be reduced via \(P = p - \dot{b} |x|^2/(4 b^3)\)  essentially moving the non-homogeneous term to the dynamic boundary condition (). This reduces (REF ) to Laplace's equation, meaning this configuration can be solved numerically with the boundary integral method [1]}. The lifting plate problem was first considered mathematically by [2]}, who demonstrated a relationship between the number of fingers that develop and the surface tension parameter. In particular, it was shown that the number of fingers is a monotonically decreasing function of time. As a point of comparison, for the traditional Hele–Shaw configuration, discussed in sec:Standard, the number of fingers typically increases with time due to tip-splitting. This behaviour was later shown to be consistent with experimental results [3]}, [4]}. We note that the case where the inviscid bubble is injected into the viscous fluid while the plates are separated has also received attention [5]}, [6]}, [7]}.
